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# 3. Simple Harmonic Motion

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#### About this Lecture

Lecture

In this mini-lecture, we introduce simple harmonic motion (SHM). As we move though this mini-lecture, we consider: (i) pendulums and springs, which both exhibit SHM; (ii) gravity and elasticity as suitable restring forces that allow for SHM in the pendulum and spring, respectively; (iii) SHM of a mass on a spring with a restoring force given Hooke’s Law F = kx; (iv) the relationship between the potential energy of a mass on a spring, which is quadratic, and the force (F = kx), which is linear; (v) the equation for acceleration of SHM systems, where we introduce angular frequency, natural frequency, and period; (vi) the equation for the acceleration of SHM, and relate it back to the displacement equation derived in mini-lecture 2; (vii) the period and frequency of the pendulum, checking the dimensions and going over an example; (viii) the period of a mass on a spring, and check the dimensions; and (ix) the relationship between the period of the pendulum and a mass on a spring, which gives an expression for the spring constant.

Course

In this course, Professor Giles Hammond (University of Glasgow) explores elasticity and oscillations. In the first mini-lecture, we consider elasticity, stress, and strain of materials when forces are applied. In the second mini-lecture, we use the simple pendulum to discuss oscillations and the corresponding displacement, velocity, and acceleration equations of the oscillating motion. In the third mini-lecture, we introduce the concept of simple harmonic motion and use two systems, the simple pendulum and a mass on a spring, to understand it’s properties. In the fourth mini-lecture we discuss damping and resonance. In the fifth mini-lecture, we bring together what we have learned in an example that covers stress, extension, and oscillation frequency of a steel wire.

Lecturer

Giles Hammond is a Professor of Experimental Gravitational Physics at the University of Glasgow. His research interests focus on the development of fused silica suspension systems for gravitational wave detectors. He has made significant contributions to the development of the monolithic stages of quadruple pendulums used in the process of updating the components used in the Laser Interferometer Gravitational-Wave Observatory (LIGO) into the experiment now deemed Advanced LIGO (aLIGO). During this process, he led the installation of several suspensions at both the Hanford and Livingston aLIGO sites. This improved precision of aLIGO contributed to the first direct detection of gravitational waves in 2015, which led to the 2017 Nobel Prize in Physics.

#### Cite this Lecture

**APA style**

Hammond, G.
(2022, January 12).
*Elasticity and Oscillations - Simple Harmonic Motion* [Video]. MASSOLIT. https://massolit.io/courses/elasticity-and-oscillations/simple-harmonic-motion

**MLA style**

Hammond, Giles.
"Elasticity and Oscillations – Simple Harmonic Motion." *MASSOLIT*, uploaded by MASSOLIT,
13 Jan 2022,
https://massolit.io/courses/elasticity-and-oscillations/simple-harmonic-motion